##### Sesión Análisis

Diciembre 14, 12:00 ~ 12:20

## Algebraic structures in linear dynamics

### Bes, Juan

A special task in linear dynamics has been to determine the existence of large algebraic structures within the set $HC(T)=\{ f\in X: \{ f, Tf, T^2f,\dots \} \mbox{ is dense in X.} \}$ of hypercyclic vectors of an operator $T$ on a Fr\'{e}chet algebra $X$. That is, when does $HC(T)$ contain (but zero) $(i)$ a dense linear subspace? $(ii)$ a closed and infinite-dimensional linear subspace? $(iii)$ a non-finitely generated subalgebra of $X$? Plenty is known about the first two questions, but no so much about the last one, of which we discuss some recent attempts to narrow this gap.

Autores: Bes, Juan / Conejero, J. Alberto / Papathanasiou, Dimitris .